Mechanisms Underlying Accuracy in Fast Goal-Directed Arm Movements in Man

Identifying coordination between joint movements during a throwing task with multiple degrees of freedom

It is known that coordination between joint movements is crucial for the achievement of motor tasks and has been studied extensively. Especially, in sports biomechanics, researchers are interested in determining which joint movements are coordinated to achieve a motor task. However, this issue cannot be easily addressed with the methods employed in previous studies. Therefore, we aimed to propose a method for identifying joint coordination. Subsequently, we examined which joint movements were coordinated using accurate overhead throwing, which required reduction in vertical hand velocity variability. Fourteen baseball players participated by attempting throwing using a motion capture system. The index of coordination for each joint movement and the effect of deviation of one joint movement on vertical hand velocity were quantified. Our results showed that the shoulder internal/external rotation angle (θ_1-IE) and the other joint movements or the shoulder horizontal flexion/extension angular velocity (ω_1-FE) and the other joint movements were coordinated. These results could be explained by the fact that the effects of the deviation of the shoulder internal rotation angle (θ_1-I) and shoulder horizontal flexion angular velocity (ω_1-F) on vertical hand velocity were larger than those of the other joint movements. This meant that it was necessary to cancel the deviations of θ_1-IE and ω_1-FE by the other joint movements. These findings indicate that the method proposed in this study enables the identification of which joint movements are coordinated in multiple degrees of freedom.

A feedback information-theoretic transmission scheme (FITTS) for modeling trajectory variability in aimed movements

Trajectories in human aimed movements are inherently variable. Using the concept of positional variance profiles, such trajectories are shown to be decomposable into two phases: In a first phase, the variance of the limb position over many trajectories increases rapidly; in a second phase, it then decreases steadily. A new theoretical model, where the aiming task is seen as a Shannon-like communication problem, is developed to describe the second phase: Information is transmitted from a "source" (determined by the position at the end of the first phase) to a "destination" (the movement's end-point) over a "channel" perturbed by Gaussian noise, with the presence of a noiseless feedback link. Information-theoretic considerations show that the positional variance decreases exponentially with a rate equal to the channel capacity C. Two existing datasets for simple pointing tasks are re-analyzed and observations on real data confirm our model. The first phase has constant duration, and C is found constant across instructions and task parameters, which thus characterizes the participant's performance. Our model provides a clear understanding of the speed-accuracy tradeoff in aimed movements: Since the participant's capacity is fixed, a higher prescribed accuracy necessarily requires a longer second phase resulting in an increased overall movement time. The well-known Fitts' law is also recovered using this approach.

Fast and fine-tuned corrections when the target of a hand movement is displaced

To study the strategy in responding to target displacements during fast goal-directed arm movements, we examined how quickly corrections are initiated and how vigorously they are executed. We perturbed the target position at various moments before and after movement initiation. Corrections to perturbations before the movement started were initiated with the same latency as corrections to perturbations during the movement. Subjects also responded as quickly to a second perturbation during the same reach, even if the perturbations were only separated by 60 ms. The magnitude of the correction was minimized with respect to the time remaining until the end of the movement. We conclude that despite being executed after a fixed latency, these fast corrections are not stereotyped responses but are suited to the circumstances.

On-line corrections for visuomotor errors

This study was designed to determine how visual feedback mediates error corrections during reaching. We used visuomotor rotations to dissociate a cursor, representing finger position, from the actual finger location. We then extinguished cursor feedback at different distances from the start location to determine whether corrections were based on error extrapolation from prior cursor information. Results indicated that correction amplitude varied with the extent of cursor feedback. A second experiment tested specific aspects of error information that might mediate corrections to visuomotor rotations: rotation angle, distance between the finger and cursor positions and the duration of cursor exposure. Results showed that corrections did not depend on the amplitude of the rotation angle or the amount of time the cursor was shown. Instead, participants corrected for the cursor-finger distance, at the point where cursor feedback was last-seen. These findings suggest that within-trial corrections and inter-trial adaptation might employ different mechanisms.

Test of Validity of Fitts' Index of Difficulty as a Measure of Task Difficulty

This study investigated the validity of Fitts' index of difficulty as a measure of task difficulty perceived by the performer. Eight subjects performed self-terminated horizontal elbow-extension movements toward targets of three indices of difficulty in two task conditions. In the target-size condition, triceps and biceps activities during acceleration and deceleration respectively decreased with increasing index of difficulty, resulting in a lower peak velocity and longer movement time. In the movement amplitude condition, however, triceps activity after movement onset and biceps activity during deceleration increased with increasing index of difficulty, resulting in a higher peak velocity. The movement time also increased as a function of the index of difficulty given increase in the distance traveled by the limb. These results suggest that Fitts' index of difficulty may not reflect the difficulty of task performance because its effect on the pattern of motor output is dependent upon the task variable manipulated in measuring the index of difficulty.

Motor variability within a multi-effector system: experimental and analytical studies of multi-finger production of quick force pulses

The purpose of the study was to develop a model of force variability for a fast action performed by a multi-effector system and to verify it for multi-finger quick force production. The experiments involved quick isometric contractions to different target force levels using different finger combinations. Force variance calculated over sets of trials for a multi-finger force production task showed non-monotonic single-peak profiles of force variance with a peak at a time between the times of the maxima of the force rate and of the total force. When analyzed in the four-dimensional space of finger forces, the variance peak was mostly expressed in the direction of the force rate, and was absent in the directions orthogonal to it. The non-monotonic time profile of the force variance could be reproduced by a model of force production, which assumes that each finger force profile is based on a template function scaled in duration and magnitude with two parameters assigned prior to each trial with some variability. The model allows decomposition of the force variance into two fractions related to variability in setting the magnitude and duration scaling parameters. The former fraction changes monotonically with time, while the latter shows a transient peak in the middle of the action. The model was able to reproduce experimental variance time profiles across conditions with the total error of under 8%. The results demonstrate, in particular, that fast multi-finger actions may show transient changes in motor variability in certain directions of the finger force space, particularly in the direction of the first force derivative, without any task-specific coordinating action by the controller. These findings require a reconsideration of some of the conclusions drawn in recent studies on the structure of motor variability in redundant multi-effector systems.

Updating Target Location at the End of an Orienting Saccade Affects the Characteristics of Simple Point-to-Point Movements

Six results are reported. (a) Reaching accuracy increases when visual capture of the target is allowed (e.g., target on vs. target off at saccade onset). (b) Whatever the visual condition, trajectories diverge only after peak acceleration, suggesting that accuracy is improved through feedback mechanisms. (c) Feedback corrections are smoothly implemented, causing the corrected and uncorrected velocity profiles to exhibit similar shapes. (d) Initial kinematics poorly predict final accuracy whatever the condition, indicating that target capture is not the only critical input for feedback control. (e) Hand and eye final variability are unrelated, suggesting that gaze direction is not a target signal for arm control. (f) Extent errors are corrected without modification of movement straightness; direction errors cause path curvature to increase. Together these data show that movements with straight paths and bell-shaped velocity profiles are not necessarily ballistic.

Repeated maximal eccentric actions causes long-lasting disturbances in movement control

This study examined acute and long-lasting effects of fatigue and muscle damage on fast and accurate elbow flexion and extension target movements (TM) with eight male students. An isokinetic machine was used to perform 100 maximal eccentric and concentric elbow flexions at 4-week intervals. Movement range was 40-170 degrees in eccentric exercise (ECCE) and 170-40 degrees in concentric exercise (CONE), with an angular velocity of 2 rad s(-1). TM was performed in sitting position with the right forearm fixed to lever arm above protractor. Subjects performed TM in horizontal plane (amplitude 60 degrees ) by visual feedback of movement from a television monitor. Surface EMG was recorded from the biceps brachii and triceps brachii muscles. TM measurements and serum creatine kinase (CK) determinations were conducted before, after, 0.5 h, 2 days, and 7 days after both exercises. Blood lactate was taken before, after, and 0.5 h after the exercises. Both ECCE and CONE led to a large decline in maximal voluntary contractions, but the recovery was slower after ECCE when it remained incomplete even until day 7 post-exercise. Lactate increased (P < 0.001) similarly after both exercises. Delayed-onset muscle soreness peaked on day 2 and CK peaked on day 7 after ECCE. Exhaustive eccentric exercise of agonistic muscles impaired the flexion TM performance, and had a long-duration modulation effect on the triphasic EMG activity pattern of flexion and extension TM. In the acute phase, the observed changes in performance and in the EMG patterns are suggested to be related to metabolic changes via III and IV muscle afferents. The delayed recovery, on the other hand, may be related to problems in the proprioceptive feedback caused by muscle damage.

Deceleration requirements and the control of pointing movements

When a limb is moved from one position to a target object, the limb and the target frequently collide. Often, the goal of the movement is to strike the target with a particular magnitude of impact. For single-aiming movements, impact forces have been shown to increase systematically with both an increased movement amplitude and a decreased movement time, thus providing deceleration to the moving limb. Models of speed-accuracy trade-off, however, have neglected to account for the contribution of these impact forces in the control of accurate movements. The aim of this experiment was to examine the modifications in the control strategy as a function of the amount of impact force a subject is allowed to use in decelerating his or her limb. Results showed that the structure of the acceleration-time functions was dictated by the amount of impact force subjects were allowed to use in decelerating the limb. Movement endpoint variability decreased as more impact force was used. The experiment suggests that the impact with a target is an important contributor to the deceleration of the moving limb and a critical determinant of movement organization.

Target and hand position information in the online control of goal-directed arm movements

The present study compared the contribution of visual information of hand and target position to the online control of goal-directed arm movements. Their respective contributions were assessed by examining how human subjects reacted to a change of the position of either their seen hand or the visual target near the onset of the reaching movement. Subjects, seated head-fixed in a dark room, were instructed to look at and reach with a pointer towards visual targets located in the fronto-parallel plane at different distances to the right of the starting position. LEDs mounted on the tip of the pointer were used to provide true or erroneous visual feedback about hand position. In some trials, either the target or the pointer LED that signalled the actual hand position was shifted 4.5 cm to the left or to the right during the ocular saccade towards the target. Because of saccadic suppression, subjects did not perceive these displacements, which occurred near arm movement onset. The results showed that modifications of arm movement amplitude appeared, on average, 150 ms earlier and reached a greater extent (mean difference=2.7 cm) when there was a change of target position than when a change of the seen hand position occurred. These findings highlight the weight of target position information to the online control of arm movements. Visual information relative to hand position may be less contributive because proprioception also provides information about limb position.

Compensatory coordination of release parameters in a throwing task

The consistency and coordination of release parameters in ball-throwing movements were investigated. The authors used a newly developed index of coordination for release parameters (ICRP) that quantifies the degree of improvement of performance consistency caused by compensatory relationships among parameters (i.e., not caused by consistency of parameters). Eight participants practiced for 150 trials, with the nondominant hand, a ball-throwing task aimed at a stationary target. The magnitude of the ball-release velocity vector, among release parameters, as well as the performance was found to become consistent with practice. The ICRP score suggested that the release parameters were complementarily coordinated with one another, and that the coordination improved with practice. Those results indicate that compensatory relationships among varying release parameters contribute to reducing the variability of performance in a ball-throwing task whose goal is accuracy.

Functional roles of the proprioceptive system in the control of goal-directed movement

This article explored functional roles of the proprioceptive system during the control of goal-directed movements. Proprioceptive information contributes to the control of movement through both reflex and central connections. Spinal and transcortical reflex loops establish a servomechanism which provides automatic corrections of unexpected changes in muscle length and allows compensation for undesirable irregularities in the mechanical properties of muscles by modulating limb stiffness at the subconscious level. Central connections provide the control system with information about peripheral states which is used in voluntary components of movement control. Before the initiation of movement, proprioceptive information about initial limb orientation becomes a basis for the programming of motor commands. During a movement, proprioceptive input about velocities and angular displacements of a limb is used to regulate movement by triggering planned sequences of muscle activation and modulating motor commands. After movement, feedback produced by responses is compared with previously stored information, verifying the quality of the movement. Considering potential roles of the reflex and central connections, the proprioceptive system seems to constitute an important aspect of motor control mechanisms, providing the control system with efficiency and flexibility in the regulation of goal-directed movements.

Evidence Supporting the Importance of Peripheral Visual Information for the Directional Control of Aiming Movement

The focus of the present study was on determining whether the high level of directional accuracy found in aiming studies in which the subjects can see their hand in the visual periphery supports the existence of a kinetic visual channel or, rather, the advantage of binocular over monocular vision for movement directional control. The limits of this kinetic visual channel were also explored. The results of the 1st experiment indicated that seeing one's hand in the visual periphery is sufficient to ensure optimal directional aiming accuracy. Further, no differences in aiming accuracy were noted between monocular and binocular vision. These results supported the existence of a visual kinetic channel. In the 2nd experiment, whether this kinetic visual channel would operate with movements slower (55°/s) than those usually used in studies that had proved its existence (over 110°/s) was determined. The results indicated that this visual kinetic channel was operative even at relatively slow movement velocities. Central vision of the hand seemed to be used for on-line directional control of relatively slow movements.

Roles of Visual Information for Control of Reaching Movements in Children

What visual information do children normally require for the control of reaching movements? How is performance affected when children do not have access to the preferred mode of perceptual information? These questions were studied in 28 children who were tested on 3 occasions: at 6, 7, and 8 years of age. The task was to pick beads, 1 at a time, from 1 cup and carry them to another cup. With the aid of a mirror arrangement and a curtain, the amount of visual information was manipulated with regard to both the target and the performing hand. The movements were monitored with an optoelectronic device (SELSPOT II) and analyzed in terms of transport and object-handling phases. Results showed that object handling required visual information on both hand and target. For the transport phase of the movement, visual information on the spatial location of the target was sufficient, and sight of the hand did not improve performance. In contrast to adult subjects, when children did not have access to the required visual information, their performances deteriorated markedly. These results indicate that from the age of 6, children use visual information for control of arm movements in a manner like that of adults, although with less accuracy and speed. However, even 8-year-old children are limited in their ability to use alternative perceptual strategies for movement control, and they therefore become less flexible and more dependent on visual information.

Afferent Information for Motor Control: The Role of Visual Information in Different Portions of the Movement

The question addressed in the present study was whether subjects (N = 24) can use visual information about their hand, in the first half of an aiming movement, to ensure optimal directional accuracy of their aiming movements. Four groups of subjects practiced an aiming task in either a complete vision condition, a no-vision condition, or in a condition in which their hand was visible for the first half [initial vision condition (IV)] or the second half of the movement [final vision condition (FV)]. Following 240 trials of acquisition, all subjects were submitted to a transfer test that consisted of 40 trials performed in a no-vision condition. The results indicated that seeing the hand early in movement did not help subjects to optimize either directional or amplitude accuracy. On the other hand, when subjects viewed their hand closer to the target, movements resulted that were as accurate as those performed under a complete vision condition. In transfer, withdrawing vision did not cause any increase in aiming error for the IV or the no-vision conditions. These results replicated those of Carlton (1981) and extended those of Bard and colleagues (Bard, Hay, & Fleury, 1985) in that they indicated that the kinetic visual channel hypothesized by Paillard (1980; Paillard & Amblard, 1985) appeared to be inoperative beyond 40deg of visual angle.

Modifications with aging in the role played by vision and proprioception for movement control

Young and older adults performed manual aiming movements to a visible target for either 40 or 200 trials. Under each level of practice, half of the subjects practiced the task under normal visual conditions (proprioception + vision [PV] condition), whereas the other half were not permitted to see their ongoing movement toward the target (proprioception-only [P] condition). Each acquisition trial was followed with knowledge of results (KR). After the last acquisition trial, all subjects were transferred to a common task in which only the target to be reached was visually available, with no KR. During acquisition, the younger subjects were found to be spatially more accurate than their older counterparts, and this was so regardless of the number of acquisition trials. Withdrawing KR during the transfer test did not modify the spatial accuracy of the subjects who had trained under the P condition. This indicates that the subjects had a reliable reference of the movement to be realized. Withdrawing vision of the moving hand and KR in the transfer test caused a significant increase in spatial error for both the older and the younger subjects. However, the increase in error was less pronounced for the older than for the younger subjects. In fact, the older subjects performed as well in the transfer test as the subjects who had trained in the P condition. This pattern of results suggests that in the transfer test, the older subjects could still guide their movements with the proprioceptive information that was available during both acquisition and transfer. However, such was not the case for the younger subjects. This suggests that, unlike the younger subjects, the older subjects could still rely on the proprioceptive cues available during acquisition in the PV condition. These results are taken to indicate that practicing with numerous sources of afferent information, as was the case in the PV condition, resulted in an integrated reference store for the younger subjects. In contrast, while practicing the task in the PV condition, the older subjects appeared to process independently from each other the different sources of sensory information available.

Analysis of kinematic invariances of multijoint reaching movement

There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations.

Variations in several mechanical parameters associated with elbow flexion during practice under different load criteria

The purpose of this study was to analyze variations in the accuracy of the moment produced by the elbow flexors during feedback-assisted acquisition of a motor skill. The task consisted of minimizing the error around three criterional levels: 20%, 30%, or 50% of the maximal isokinetic concentric moment of these muscles measured at 90 degrees/sec. Healthy women, aged 22 to 30 years, were divided into three groups (nA = 6, nB = 6, nC = 4) corresponding to the above criteria. They were asked to perform 10 sets of 10 right-elbow flexions per day over a period of three consecutive days. The results indicated a significant difference among the groups mainly in terms of overshooting (Group A) or undershooting (Group C) the criterion. On the other hand, Group B subjects performed optimally as indicated both by a significant convergence to the criterion (30%) and a comparatively small number of repetitions required for achievements. These findings demonstrate the existence of an optimal performance point which is located at about 30% of the maximal isokinetic concentric moment.

Control of Rapid Arm Movements When Target Position Is Altered During Saccadic Suppression

This experiment examined whether rapid arm movements can be corrected in response to a change in target position that occurs just prior to movement onset, during saccadic suppression of displacement. Because the threshold of retinal input reaches its highest magnitude at that time, displacement of the visual target of a saccade is not perceived. Subjects (N = 6) were instructed to perform very rapid arm movements toward visual targets located 16, 20, and 24 degrees from midline (on average, movement time was 208 ms). On some trials the 20 degrees target was displaced 4 degrees either to the right or to the left during saccadic suppression. For double-step trials, arm movements did not deviate from their original trajectory. Movement endpoints and movement structure (i.e., velocity-and acceleration-time profiles) were similar whether or not target displacements occurred, showing the failure of proprioceptive signals or internal feedback loops to correct the arm trajectory. Following this movement, terminal spatially oriented movements corrected the direction of the initial movement (as compared with the single-step control trials) when the target eccentricity decreased by 4 degrees. Subjects were unaware of these spatial corrections. Therefore, spatial corrections of hand position were driven by the goal level of the task, which was updated by oculomotor corrective responses when a target shift occurred.

Planning for hand shape and arm transport when reaching for objects

Two early components of object manipulation are shaping the hand appropriately for functional interaction and transporting the arm with appropriate force and spatial precision to the target object. Three experiments addressed whether people plan these two components before the onset of reaching and if so, how the plans are coordinated. Subjects reached for and contacted a series of objects with one of four hand configurations: pinch, poke, palm, and clench. The required configuration was signaled by the object's color; in some conditions its structure provided a redundant cue. The time from object exposure to arm liftoff (reaction time: RT) and the time from liftoff to contact (movement time: MT) were recorded. In Experiment 1, a compatible stimulus-to-hand-shape mapping substantially facilitated RT but not MT, suggesting that the appropriate hand shape was planned prior to reaching. Experiment 2 showed that contact precision, as defined by the stability of the object's support plane, affected MT; a smaller RT effect also suggested some pre-movement planning of arm transport to accommodate precision demands. Experiment 3 combined compatibility and precision manipulations in a single task to test a model which proposes that planning for hand-shape and arm transport occur in parallel, with the onset of reaching deferred until the slower planning process is completed.

The effect of viewing the static hand prior to movement onset on pointing kinematics and variability

Pointing accuracy and arm movement kinematics of six human subjects were measured in three conditions where the hand was never visible during the ongoing movement: (1) in the dark; (2) the static hand was seen in peripheral vision prior to target presentation, but not during the reaction time (H-T); (3) the static hand was seen in peripheral vision until movement onset (H+T). It was shown that: (1) viewing the hand prior to movement decreased pointing variability as compared to the dark condition. (2) Viewing simultaneously hand and target (H+T) and further decreased pointing variability as compared to the H-T condition. This effect was proportional to the reaction time. (3) A lengthening of the deceleration phase was observed for movements performed in the H+T condition, as compared to the other two conditions. (4) A negative correlation between variability and the first part of the deceleration phase was observed in the H+T condition, but neither in the H-T condition nor in the dark. These results suggest that the decrease in pointing variability observed in the H+T condition is due to a feedback based on kinesthetic reafference. Better encoding of the initial position of the hand relative to the target (as in H+T) would allow a calibration of arm position sense, which is used to drive the hand toward the target during the deceleration phase.

Determining Movement Onsets from Temporal Series

With the advent of recent measurement techniques, kinematic and kinetic measures commonly are used to describe events over time. Often, the central and peripheral nature of the control processes involved are derived from these temporal series. For example, movement onset often arbitrarily defines the end of the central and the beginning of the peripheral processes. Because of its critical temporal location, we examined whether response dynamics (average movement velocity) affects the determination of movement onset. Interactive graphics and numerical methods of determining movement onsets from temporal series were evaluated on various kinematic signals. Variations in the initial rate of change in a given signal significantly affected the determination of movement onset. Consequently, measurements of component latency must be regarded with caution. A cursory description of related problems elucidated in previous research is discussed, and procedures that can minimize these artifacts are suggested.

Visuomotor performance of normal and clumsy children. I: Fast goal-directed arm-movements with and without visual feedback

The mechanisms underlying accuracy in fast goal-directed arm-movements were investigated in normal and clumsy children in two age-groups, six to seven and 10 to 11 years. Clumsy children in both age-groups had a longer movement time than normal children; this difference increased slightly when there was visual feedback. For both normal and clumsy children, the relative variability of the total distance moved was smaller than that of the distance moved during acceleration, indicating a variability reduction mechanism in the course of a movement. In the six- to seven-year-old group, the relative variability of the distance moved during acceleration and of the total distance was larger for clumsy than for normal children; this did not reach significance in the 10- to 11-year-old group. It is suggested that motor difficulties are linked to inaccuracy in open-loop control processes and to less efficient use of visual feedback.

Arm-Tracking Performance With and Without Visual Feedback in Children and Adults

Tracking performance was investigated in children (aged 6-7 and 10-11) and in adult subjects. Target signals, moving unpredictably along a straight line, were tracked with the preferred arm, alternately with and without visual feedback. Qualitative observations indicate that tracking is based on continuous adjustments of the ongoing response to the continuously changing target position. No step-and-hold strategy could be detected in any of the three age groups. Tracking performance was described with four simple parameters, derived from linear systems analysis: (a) the delay between target signal and tracking movement (DL); (b) performance at the low-frequency range (LF), (c) performance at the high-frequency range (HF); and (d) a measure of tracking quality or overall similarity in the shape of target signal and tracking movement (Q). There was a considerable improvement in tracking performance with age, even after the age of 10-11, which was mainly demonstrated by a decrease in DL and increases in HF and Q. Tracking performance decreased only to a small extent when visual feedback was withdrawn. Age-related differences in the contribution of visual feedback to tracking performance could not be demonstrated.